Of course it is.

It is censorship, they're just censoring their own ears, and maybe trying to censor the ears of others. If they're censoring their own ears, then i'm ok with that. It's their station, and they can run it how they want. It's still censorship though, say you don't like the word "cramp", and you tell people not so say it around you. You're censoring what comes into your own ears. The question is; is it censoring or not, not whether or not I agree with censoring.

By definition it is.

They are banning something that they do not want to be heard. This is censorship. Now, what we must examine is whether or not they should be able to ban something. They are not censoring freedom of speech, as someone could still say whatever they want, they just do not have to be given a platform for their beliefs. If they wish to market to groups that do not wish to hear profanities, then they should not have to allow profanities.

It is not censorship

Censorship is dictated by the State. Private radio stations can choose to play what they wish because it is privately owned. It is not censorship due to the fact that how a business is run is up to the owners of the private firm. If they wish not to have certain a type of music or program that is their choice. But other companies will retain the ability to play a song or a program that other companies may find deplorable. The State is the only censor.

It's a private company with their own policy

If a radio station is playing lyrics that are inappropriate and parents call the stations complaining and they decide to put it down, that's democratic. It's not censorship because they're not banning anything. What they are doing is saying they won't have a song played on their airwaves. That's the difference. Same with a family network. By nature they are family oriented so they won't play anything really explicit, much like HBO Family.

No, it is not censorship to prohibit profanity.

Censorship in my opinion is when someone controls the content of what is going out on the air. Not allowing profanity only disallows a couple of words. It does not change the content of the message that is being broadcast. The important thing is that whatever message is being sent out, it is unaffected by the lack of profanity.

No it isn't

Provided they warn people that they don't tolerate swearing, that is obviously a free choice, and a choice to disallow certain words from being said by a private organization is not really something that I or most other people would define as "censorship".